Answer:
The 95% confidence interval for the percent of all black adults who would welcome a white person into their families is (0.8222, 0.8978).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of 
, and a confidence level of 
, we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of 
.
For this problem, we have that:
323 blacks, 86% of blacks said that they would welcome a white person into their families. This means that 
95% confidence level
So 
, z is the value of Z that has a pvalue of 
, so 
.
The lower limit of this interval is:
The upper limit of this interval is:
The 95% confidence interval for the percent of all black adults who would welcome a white person into their families is (0.8222, 0.8978).
Answer:
The values of x for which the model is 0 ≤ x ≤ 3
Step-by-step explanation:
The given function for the volume of the shipping box is given as follows;
V = 2·x³ - 19·x² + 39·x
The function will make sense when V ≥ 0, which is given as follows
When V = 0, x = 0
Which gives;
0 = 2·x³ - 19·x² + 39·x
0 = 2·x² - 19·x + 39
0 = x² - 9.5·x + 19.5
From an hint obtained by plotting the function, we have;
0 = (x - 3)·(x - 6.5)
We check for the local maximum as follows;
dV/dx = d(2·x³ - 19·x² + 39·x)/dx = 0
6·x² - 38·x + 39 = 0
x² - 19/3·x + 6.5 = 0
x = (19/3 ±√((19/3)² - 4 × 1 × 6.5))/2
∴ x = 1.288, or 5.045
At x = 1.288, we have;
V = 2·1.288³ - 19·1.288² + 39·1.288 ≈ 22.99
V ≈ 22.99 in.³
When x = 5.045, we have;
V = 2·5.045³ - 19·5.045² + 39·5.045≈ -30.023
Therefore;
V > 0 for 0 < x < 3 and V < 0 for 3 < x < 6.5
The values of x for which the model makes sense and V ≥ 0 is 0 ≤ x ≤ 3.
Answer:
226
Step-by-step explanation:
Area of rectangle:
x+6=17
x=11
11+6=17
11+3=14
17×14=238
Area of triangle:
Use phytagoras theorem to find the base of the triangle:
c²=a²+b²
5²=4²+b²
25=16+b²
b²=25-16
b²=9
b=√9
b=3 (only the half)
b=6 (the whole base)
3×4
12
Shades region:
238-12
=226
Answer:
Step-by-step explanation:
Combine real terms and combine complex terms
1) 3 + 2i + 2 - 5i = 3 +2 + 2i - 5i
= 5 + (2-5)i
= 5 + (-3)i
= 5 - 3i
3) 2 - (1 - 2i) + (4 -5i ) - (1 - 3i) = 2 -1 + 2i + 4 - 5i - 1 + 3i
{- is distributed to (1 - 2i) & - is distributed to (1- 3i)}
= 2 - 1 + 4 + 1 + 2i - 5i + 3i
= 6 +0i = 6
5) 4 - 3i + 4 + 3i = 4 +4 -3i + 3i
= 8
7) (3 - 2i)² + (3 +2i) = 3² - 2*3*2i + (2i)² + 3 + 2i {(a - b)² = a² - 2ab +b²}
= 9 -12i + 4i² + 3 + 2i
= 9 - 12i + 4*(-1) + 3 + 2i {i² = -1}
= 9 +3 - 4 - 12i +2i
= 8 - 10i
